FAST CALCULATION OF ALL STABILIZING GAINS FOR DISCRETE-TIME SYSTEMS

Öz

In this paper, two methods for calculating all stabilizing gains for discrete-time systems are given. The first method focuses on converting the problem using a bilinear transformation and then applying a previously developed theorem for continuous time systems. Unlike previous results, the method introduced here does not use the Generalised Hermite-Biehler Theorem and therefore provides a computational advantage. The second method demonstrates the use of  Chebyshev Polynomials in the solution of the problem

Anahtar Kelimeler

• Bilinear Transformation, Nyquist’s Criterion, Chebyshev Polynomials

Kaynakça

1. Ackermann, J., Kaesbauer, D., Bajcinca, N., “Discrete-Time Robust PID And Three Term Control”, XV IFAC World Congress, Barcelona, Datta, A., Ho, M.T., Bhattacharyya S.P., Structure and Synthesis of PID Controllers, Springer, London, UK, 2000.
2. Ho, M.T., Datta, A., Bhattacharyya S.P., “ A Linear Programming Characterization Of All Stabilizing PID Controllers”, Proceedings of the Amer. Contr. Conf., pp. 3922-3928, 1997.
3. Keel, L., Bhattacharyya S.P., “Root Counting and Phase Unwrapping With Respect To The Unit circle with applications”, Proc of the 40th IEEE Conf. on Decision and Control, Orlando, Florida USA, pp. 3459-3464, 2001.
4. Keel, L., Bhattacharyya S.P., “Root Counting and Phase Unwrapping Stability And Stabilization Of Discrete Time Systems”, Linear Algebra And Its Applications, Vol. 351, No. 352, pp. 501-517, 2002.
5. Munro, N., Söylemez, M.T., Baki, H., “Computation Of D-Stabilizing Low-Order Compensators”, Control Systems Centre Report, , UMIST Manchester, 1999.
6. Munro, N., Söylemez, M.T.,“Fast Calculation Of Stabilizing PID Controllers For Uncertain Parameter Systems”, IFAC ROCOND, Prague, Czech Republic , 2000.
7. Söylemez, M.T., Munro, N., Baki, H., “Fast Calculation Of Stabilizing PID [10] Fox, L., Parker, I.B., Chebyshev Controllers”, Automatica, Vol: 39, No: 1, pp. 121-126, 2003.
8. Xu, H., Datta, A., Bhattacharyya S.P., “Computation Of All Stabilizing PID Gains For Digital Control Systems”, IEEE Transactions On Automatic Control. Vol: 46 No: 4, pp. 647-652, Oxford University Press, London, 21-64, 1968.